Pls fans help me out with this problem........n^{3}/square root n+1
Assuming the OP meant to write $\displaystyle \displaystyle \begin{align*} \int{ \frac{ n^3 }{ \sqrt{ n + 1 }}\,dn} \end{align*}$, a substitution of the form $\displaystyle \displaystyle \begin{align*} u = n + 1 \implies du = dn \end{align*}$ is appropriate, giving
$\displaystyle \displaystyle \begin{align*} \int{ \frac{n^3}{\sqrt{n+1}}\,dn} &= \int{ \frac{\left( u - 1 \right) ^3}{\sqrt{u}}\,du} \end{align*}$
Now expand the numerator, divide each term by $\displaystyle \displaystyle \begin{align*} u^{\frac{1}{2}} \end{align*}$, and integrate.